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Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints

Author

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  • Yan-Chao Liang

    (Henan Normal University)

  • Jane J. Ye

    (University of Victoria)

Abstract

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems with important applications. It is well known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail. To deal with this issue, one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper, we first survey recent results on constraint qualifications and optimality conditions for MPDC, then apply them to MPSC. Moreover, we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC, and the other is obtained via the local decomposition approach.

Suggested Citation

  • Yan-Chao Liang & Jane J. Ye, 2021. "Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 1-31, July.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:1:d:10.1007_s10957-021-01879-y
    DOI: 10.1007/s10957-021-01879-y
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    References listed on IDEAS

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    1. Falk Hante & Sebastian Sager, 2013. "Relaxation methods for mixed-integer optimal control of partial differential equations," Computational Optimization and Applications, Springer, vol. 55(1), pages 197-225, May.
    2. Lei Guo & Jin Zhang & Gui-Hua Lin, 2014. "New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 737-754, December.
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    Cited by:

    1. Jinman Lv & Zhenhua Peng & Zhongping Wan, 2021. "Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    2. Kin Keung Lai & Shashi Kant Mishra & Sanjeev Kumar Singh & Mohd Hassan, 2022. "Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems," Mathematics, MDPI, vol. 10(15), pages 1-16, August.

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